Advanced Topics of Stochastics
Fortgeschrittene Themen der Stochastik
6 LPunregelmäßigEN
Voraussetzungen
Empfohlen, im Wortlaut
Knowledge of the contents of modules • 11217: Wahrscheinlichkeitstheorie, • 11103: Analysis I, • 11104: Analysis II and • 11101: Lineare Algebra and Analytische Geometrie I or good knowledge of the contents of modules • 11917: Mathematik W-3 (Statistik) or 11217: Wahrscheinlichkeitstheorie • 11213: Mathematik IT-3 (Analysis) and • 11113: Mathematik IT-2 (Lineare Algebra)
Inhalte
Course topics include (but are not limited to): • stochastic simulation (e.g. Markov Chain Monte Carlo, simulated annealing, sensitivity analysis) • time series analysis (e.g. regression models, autoregressive processes, estimation and prediction) • uncertainty quantification (e.g. entropy and information, inverse problems, Kalman filters) • Monte Carlo methods for partial differential equations (e.g., diffusion processes Feynmac-Kac formulae) • modelling extreme events (z.B. extreme value theory, large deviations, theory of risk)
Lernziele
After successfully completing the module, students have in-depth knowledge in the field of stochastics. They are able to assess the aims and scope of probability models and related numerical methods. Using specific applications, students have gained experience in independent scientific work.
Prüfungsleistung
Prerequisite: • Successful completion of exercises Final module examination: • Oral examination, 30 min.
Literatur (4)
- S. Asmussen, P.W. Glynn. Stochastic Simulation: Algorithms and Analysis, Springer, 2007.
- P.J. Brockwell, R.A. Davis. Introduction to Time Series and Forecasting. Springer, 2010.
- E. Pardoux. Markov Processes and Applications, Wiley, 2008.
- S. Reich, C. Cotter. Probabilistic Forecasting and Bayesian Data Assimilation. Cambridge University Press, 2015.
Bemerkungen
• Study programme Mathematics M.Sc.: Compulsory elective module in the complex „Stochastics” • Study programme Mathematical Data Science M.Sc.: Compulsory elective module in the complex „Advanced Mathematical Methods in Data Science” • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung”, in limited extend • Study programme Wirtschaftsmathematics B.Sc.: Compulsory elective module in complex „Vertiefung”, in limited extend • Study programme Informatik B.Sc.: Compulsory elective module in complex „Mathematik”. • Study programme Informatik M.Sc.: Compulsory elective module in complex „Mathematik” or in field of application „Mathematik”
Quelle: Modulbeschreibung der BTU · abgerufen 29.09.2026Original